of stochasticity that can affect population persistence can be grouped into four main categories: demographics, environment, natural catastrophes, and genetics (Shaffer 1981).

Demographic Stochasticity

Demographic stochasticity refers to the chance variation in survival and reproductive rates in very small populations (for example, the probability that all individuals in a population will not reproduce in a given period). Although average values for survival or reproduction might remain relatively constant, chance variation can occur among individuals. As a simple example, consider an annually reproducing population with nonoverlapping age classes, whose average probability of survival to reproduction is 0.20. Despite this average survival rate, if the population is extremely small—say, 10 individuals—there is a probability of about 11% in any one year that all members of the population will die before reproducing, in which case the population will go extinct. If the population is somewhat larger–say, 50 individuals–the probability that the population will go extinct during a given year is very low, less than 0.002%. Equally important is that the probability of demographic extinction is associated with just a single “trial” (that is, a single year). As the “demographic dice” are cast each year, the cumulative probability of chance extinction increases as a simple arithmetic product of the probabilities for all consecutive years if the population does not increase. Although the numerical threshold where demographic stochasticity can cause extinction depends on the particular situation, a threshold estimate for dioecious organisms of about 50 individuals is widely cited (Pollard 1966, Keiding 1975, Shaffer 1981). The fate of a population for which this type of stochastic process becomes important is bleak; as noted by Gilpin and Soulé (1986), demographic stochasticity might well be viewed as “the immediate precursor of extinction.”

Environmental Stochasticity

Environmental stochasticity usually reflects the impact of random variation in the environment as it influences a population. In its simplest form, the demographic effects of environmental perturbations are assumed to be equally distributed across all individuals in a particular age or stage class in a population. For example, an increase in seed predators might reduce average reproductive output by 80% in a plant population; this decrease, because it represents a drop in average reproductive output across all individuals in the reproductive age class, can severely reduce the size of the population, regardless of its initial size. Because of its capacity to adversely affect even large populations, environmental stochasticity is considered an important force in promoting chance extinction (Sykes 1969, Cohen 1979, Leigh 1981, Menges 1990, 1991). In essence, envi-

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